Basic Statistical Analysis

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This user-friendly, readable revision is presented as simply as possible to ensure that students will gain a solid understanding of statistical procedures. The goal of this book is to demystify statistics. The student is presented with rules of evidence and the logic behind those rules. The book is divided into three major units: Descriptive Statistics, Inferential Statistics, and Advanced Topics in Inferential Statistics.

Preface

vii

UNIT I DESCRIPTIVE STATISTICS

1

(126)

1 Introduction to Statistics

3

(16)

Stumbling Blocks to Statistics

4

(8)

A Brief Look at the History of Statistics

12

(2)

Benefits of a Course in Statistics

14

(1)

General Field of Statistics

14

(2)

Summary

16

(1)

Key Terms and Names

17

(1)

Problems

17

(2)

2 Graphs and Measures of Central Tendency

19

(24)

Graphs

19

(7)

Measures of Central Tendency

26

(9)

Appropriate Use of the Mean, the Median, and the Mode

35

(4)

Summary

39

(1)

Key Terms

40

(1)

Problems

40

(2)

Computer Problems

42

(1)

3 Variability

43

(18)

Measures of Variability

44

(9)

Graphs and Variability

53

(3)

Summary

56

(1)

Key Terms

57

(1)

Problems

57

(3)

Computer Problems

60

(1)

4 The Normal Curve and z Scores

61

(24)

The Normal Curve

61

(4)

z Scores

65

(8)

Translating Raw Scores into z Scores

73

(4)

z Score Translations in Practice

77

(5)

Summary

82

(1)

Key Terms and Names

82

(1)

Problems

82

(3)

5 z Scores Revisited: T Scores and Other Normal Curve Transformations

85

(22)

Other Applications of the z Score

85

(1)

The Percentile Table

86

(9)

T Scores

95

(3)

Normal Curve Equivalents

98

(1)

Stanines

98

(1)

Grade-Equivalent Scores: A Note of Caution

99

(3)

The Importance of the z Score

102

(1)

Summary

103

(1)

Key Terms

104

(1)

Problems

104

(3)

6 Probability

107

(20)

The Definition of Probability

107

(7)

Probability and Percentage Areas of the Normal Curve

114

(5)

Combining Probabilities for Independent Events

119

(3)

A Reminder about Logic

122

(1)

Summary

122

(1)

Key Terms

123

(1)

Problems

123

(4)

UNIT II INFERENTIAL STATISTICS

127

(236)

7 Statistics and Parameters

129

(27)

Generalizing from the Few to the Many

129

(1)

Key Concepts of Inferential Statistics

130

(2)

Techniques of Sampling

132

(8)

Sampling Distributions

140

(8)

Back to z

148

(3)

Some Words of Encouragement

151

(1)

Summary

151

(1)

Key Terms

152

(1)

Problems

152

(4)

8 Parameter Estimates and Hypothesis Testing

156

(23)

The Standard Deviation Revisited

156

(2)

Estimating the Standard Error of the Mean

158

(1)

Estimating the Population Mean: Interval Estimates and Hypothesis Testing

159

(1)

The t Ratio

160

(5)

The Type 1 Error

165

(1)

Alpha Levels

166

(3)

Effect Size

169

(1)

Interval Estimates: No Hypothesis Test Needed

170

(4)

Summary

174

(1)

Key Terms

174

(1)

Problems

175

(2)

Computer Problems

177

(2)

9 The Fundamentals of Research Methodology

179

(40)

Research Strategies

180

(1)

Independent and Dependent Variables

181

(2)

The Causes and-Effect Trap

183

(1)

Theory of Measurement

184

(5)

Research: Experimental versus Post-Facto

189

(1)

The Experimental Method: The Case of Cause and Effect

189

(3)

Creating Equivalent Groups: The True Experiment

192

(2)

Designing the True Experiment

194

(3)

The Hawthorne Effect

197

(1)

Sequencing Effects

198

(1)

Counterbalancing

198

(1)

Repeated Measures Designs with Separate Control Groups

199

(2)

Requirements for the True Experiment

201

(1)

Post-Facto Research

202

(3)

Combination Research

205

(1)

Research Errors

206

(2)

Experimental Error: Failure To Use an Adequate Control Group

208

(1)

Post-Facto Errors

209

(2)

Meta-Analysis

211

(2)

Methodology as a Basis for More Sophisticated Techniques

213

(1)

Summary

213

(2)

Key Terms

215

(1)

Problems

216

(3)

10 The Hypothesis of Difference

219

(36)

Sampling Distribution of Differences

220

(3)

Estimated Standard Error of Difference

223

(2)

Two-Sample t Test for Independent Samples

225

(3)

Significance

228

(4)

Two-Tail t Table

232

(2)

Alpha and Confidence Levels

234

(2)

The Minimum Difference

236

(1)

Outliers

236

(1)

One-Tail t Test

237

(4)

Importance of Having at Least Two Samples

241

(1)

Power

242

(1)

Effect Size

243

(4)

Summary

247

(1)

Key Terms

248

(1)

Problems

249

(3)

Computer Problems

252

(3)

11 The Hypothesis of Association: Correlation

255

(40)

Cause and Effect

255

(3)

The Pearson r

258

(1)

Interclass versus Intraclass

258

(17)

Correlation Matrix

275

(2)

The Spearman r(s)

277

(7)

An Important Difference between the Correlation Coefficient and the t Test

284

(1)

Summary

284

(1)

Key Terms and Names

285

(1)

Problems

285

(6)

Computer Problems

291

(4)

12 Analysis of Variance

295

(37)

Advantages of ANOVA

295

(2)

Analyzing the Variance

297

(14)

Applications of ANOVA

311

(1)

The Factorial ANOVA

312

(7)

Eta squared and d

319

(1)

Graphing the Interaction

320

(4)

Summary

324

(1)

Key Terms and Names

325

(1)

Problems

325

(4)

Computer Problems

329

(3)

13 Nominal Data and the Chi Square

332

(31)

Chi Square and Independent Samples

331

(11)

Locating the Difference

342

(2)

Chi Square and Percentages

344

(2)

Chi Square and z Scores

346

(1)

Chi Square and Dependent Samples

346

(6)

Requirements for Using the Chi Square

352

(1)

Summary

352

(1)

Key Terms and Names

353

(1)

Problems

353

(6)

Computer Problems

359

(4)

UNIT III ADVANCED TOPICS IN INFERENTIAL STATISTICS

363

(162)

14 Regression Analysis

365

(37)

Regression of Y on X

365

(12)

Standard Error of Estimate

377

(3)

Confidence Interval Equation

380

(1)

Multiple R (Linear Regression with More Than Two Variables)

381

(7)

Path Analysis, the Multiple R, and Causation

388

(1)

Partial Correlation

389

(4)

Summary

393

(1)

Key Terms and Names

394

(1)

Problems

394

(5)

Computer Problems

399

(3)

15 Repeated-Measures and Matched-Subjects Designs with Interval Data

402

(30)

Problem of Correlated or Dependent Samples

402

(2)

Repeated Measures

404

(1)

Paired t Ratio

404

(12)

Within-Subjects F Ratio

416

(3)

Within-Subjects Effect Size

419

(2)

Testing Correlated and Experimental Data

421

(1)

Summary

422

(1)

Key Terms

423

(1)

Problems

423

(5)

Computer Problems

428

(4)

16 Nonparametrics Revisited: The Ordinal Case

432

(16)

Mann-Whitney U Test for Two Ordinal Distributions with Independent Selection

433

(3)

Kruskal-Wallis H Test for Three or More Ordinal Distributions with Independent Selection

436

(2)

Wilcoxon T Test for Two Ordinal Distributions with Correlated Selection

438

(2)

Friedman ANOVA by Ranks for Three or More Ordinal Distributions with Correlated Selection